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Chapter 4: Problem 43

Evaluate the trigonometric function of the quadrant angle, if possible. $$\csc \pi$$

Short Answer

Expert verified
\csc(\pi) is undefined.

Step by step solution

01

Setup

We need to evaluate the function \csc(\pi). The cosine function is defined as \csc(\theta) = 1/\sin(\theta).
02

Evaluate the sine function

Now we need to evaluate the sine at \pi radians. Remember, in the unit circle, the angle \pi radians corresponds to the angle 180 degrees. At this point, the \sin value is 0.
03

Evaluate the cosecant function

As \csc(\theta) = 1/\sin(\theta), substituting \sin(\pi)=0 gives \csc(\pi) = 1/0.
04

Conclusion

As division by zero is undefined in mathematical operations, \csc(\pi) is undefined.

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